Mrs Yeo had a sum of money. She gave her daughter $400 and gave ¹₄ of the remaining money to her mother. She used ³₄ of the rest of the money on a television and was left with ¹₈ of the amount she had at first. What was the sum of money she had at first?

Her daughter	Her mother	Remaining amount		Total
$400	1x4	3x4
		Television	Left
		3x3	1x3
7x3 = 21 u			1x3 = 3 u
8 u	4 u	9 u	3 u	24 u

Fraction of the remaining amount left 
= 1 - ³₄
= ¹₄

The remaining amount is repeated.  Make the remaining amount the same. LCM of 3 and 4 is 12. 

The amount left is repeated.  Make the amount left the same.

¹₄ Remaining amount = ¹₈ Total amount

Amount that Mrs Yeo gave to her daughter
= 21 u - 4 u - 9 u
= 8 u

8 u = 400

1 u = 400 ÷ 8 = 50

Total amount that Mrs Yeo had at first
= 8 u + 4 u + 9 u + 3 u
= 24 u
= 24 x 50
= $1200

Answer(s): $1200